Time series are data observed over time (either in continuous time or at discrete time periods).

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Sample Mean of AR(1) model

Consider the AR(1) model with iid innovations with finite mean and variance. Also, let $X_0 = 0$. \begin{align} X_t = \phi X_{t-1} + \epsilon_t \end{align} The goal is to derive the asymptotic ...
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What is an appropriate statistical test to identify significantly different timepoints in two timecourses?

I have two timecourses. Both are the same length. Both are univariate. Each represents the average EEG signal from a unique subgroup. The two subgroups do not have the same number of subjects. I ...
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44 views

Model for probability of song reaching top 10 ranking, over time?

I'm trying to model the probability of a song reaching Billboards top 10 over time. My data has the columns "Day since release", "If reached top 10". For example, [12,1] means the song hit top 10 on ...
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27 views

Residual autocorrelation versus lagged dependent variable

When modeling time series one has the possibility to (1) model the correlational structure of the error terms as e.g. an AR(1) process (2) include the lagged dependent variable as an explanatory ...
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10 views

analysing multiple individuals in specific time points for similarities

I am looking for a suitable analysis to examine my data for the presence of foraging individuals at different time periods, and whether the individual are in the same place over time. My dataset is ...
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15 views

How can I a “multiplier effect” in time series data?

I currently have data corresponding to how often a certain set of songs were downloaded. Each song has a release date, and then the number of downloads per day going forward to today. It would look ...
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29 views

R, arima() with include.mean=TRUE, still has no mean reported

I have a regression with ARMA errors, which I am fitting with arima(). I know that the ARMA model is being fit on these residuals from the regression. My problem is ...
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47 views

Arima with xreg, rebuilding the fitted values by hand

I'm using R to do some time series estimation. I'm trying to rebuild the fitted values from an Arima model by hand to use in an Excel spreadsheet using the estimated coefficients and the input data. ...
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43 views

Probability of Achieving a Count Level in Time Series Data

I have some time-series data that displays a count value for every day: These count values begin at 1 or -1 and will continue to count up (or down) if conditions in the time series are met. If the ...
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20 views

Guides to VARMA modelling in R

I'm looking at using a VARMA model to both determine the driver so value in some advertising campaigns and also to forecast future activity. I'm looking at the paper by Takada and Bass as a reference ...
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25 views

Naive forecasting

I used to know that Naive forecast is equal ( ft is the same like the previous year) Someone told me that there is another equation used in the sales which is equal ( current year - previous year)/ ...
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26 views

Statistical method to compare time-series with different periods

I have 2 study areas Study area 1: 12 meteorological stations-years available 1981-2000(same data and step) Study area 2: 10 meteorological stations-years available 1985-2011(same data and step) ...
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combining and contrasting time course GLMs using R

I am analyzing some time course data in which I have set up a GLM using R for each subject. Each GLM I want to run is an attempt to extract estimates of different behavioral conditions effects on the ...
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191 views

Intervention With Differencing

When conducting an intervention analysis with time series data (aka Interrupted Time series) as discussed here for example one requirement I have is to estimate the total gain (or loss) due to the ...
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Determining parameters in AR model for non-stationary time series

I am currently trying to fit an AR model to some financial data. The time series $Y_t$ in levels is clearly non-stationary; however it appears the first differences $dY_t$ are stationary (and this is ...
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169 views

Steps to perform time series analysis

I'm trying estimate an autoregressive model with an exogenous variable. It's about the impact of changes in oil prices on the economy. I'm planning on regressing gdp growth rate on its own lagged ...
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70 views

ARIMA, adjustments and intervention analysis

I have very little knowledge of time-series analysis (despite my stat master - didn't do anything else than an introductory course) but now I'm facing a statistical problem whose answer is this very ...
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1answer
38 views

Is the Durbin-Watson test appropriate for count data

In determining if there is any serial correlation in a time series of count data, is the Durbin-Watson statistic or similar approaches appropriate? I ask this question because the dwtest implemented ...
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16 views

joint p.d.f. of stationary time series variables

if a stationary time series verifies that each variable depends only on the variable before it, and the joint p.d.f. of xi and xi-1 is f(xi-1,xi), which is the joint p.d.f. of xi,xi+1,xi+2, and of ...
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35 views

stationary time series example

Please, could anyone give an example of a stationary time series? I mean, if for instance $x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$, $x_{5}$ are the 5 first random variables of the series, what would be the ...
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19 views

Statistical thresholds for large time-series

I am working with matrices, of the size N*M, where each cell corresponds to the Pearson's correlation between two time series. I want to threshold each matrix such that it would retain only ...
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20 views

Forecasting ar(p) for several counties

I have a data set of prices, these prices vary across time and across area. I have 18 areas with 32 time periods. What i want to do is forecast these prices, i have found that a AR(3) process fits ...
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58 views

Variance of $\bar x$, simulation with non-iid observations

So I know that the variance of $\bar x$ is usually computed as $\frac{\sigma_x^2}{n}$, and that this assumes the observations are independent. If instead, the observations have some positive serial ...
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22 views

Obtaining the Psi Weights of a seasonal ARIMA in R

I am trying to quantify the effect of a future random shocks on my seasonal ARIMA model. If I have understood the theory correctly, the easiest way is to express my seasonal ARIMA model in its "random ...
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31 views

What is the best test to estimate the correlation between binomial/categorical dataset?

I'm trying to analyze if there are correlations between binomial dataset. I have binomial data (presence/absence) of two variables in different periods and I need to know what is the best way to find ...
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65 views

Standard techniques for forecasting revenue growth of a company?

I was curious what sort of time series models were the standard for doing this type of analysis. I have weekly sales data for the company - I could cook up my own time series model but would like to ...
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20 views

training period selection forecast (error analysis)

I have been lately testing the best training period length to perform a forecast. I have tested it for various days of training period length, among them 60 days and 30 days. My methodology is quite ...
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24 views

Statistical Methods for Calculating Vending Machine Refill

Am looking into statics to help support a project I am undertaking. The project scope concerns intelligent replenishment / refill of vending machines. During an onsite service, a technician must ...
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38 views

How to normalize time series?

This is a general question on normalization of data so that all the variables are within the same range. Why do we normalize data in pattern classification? How to normalize time series which is ...
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69 views

Is PCA appropriate for comparing subsets of panel data?

I have a large panel (5000+ subjects, 4 variables over 182 periods), and I've identified particular Granger-causal relationship in a large subset of those subjects (30% or so). I would like to somehow ...
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31 views

R function which uses innovations algorithm?

I can't seem to find much info on the following: I have a dataset D at time t which I use to fit an ARIMA model. I forecast the value of the time series at time t + 1. Now, when I'm in t + 1, I would ...
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22 views

Determine the threshold value and number of regimes with delayed variable

I am currently working on a threshold model for the exchange rate between UK and US. I have not got background knowledge on this model so I am really stuck on how to determine the Threshold value, ...
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51 views

Using AIC to determine best ARIMA Model

I'm trying to fit an ARIMA model to housing data set. Playing around with the p's and q I was able to get an ARIMA Model (2,1,2,)(2,0,0) with an AIC value of AIC=4946.76 I used auto.arima to see if I ...
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9 views

Approaches to Subsampling to exceed a Population Mean

I've studied a large amount of Probability & Statistics, but I'm embarrassed to say I've forgotten too much of it. Would appreciate any pointers anyone has about this: I have a set of about 360 ...
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106 views

Intervention Analysis - Pulse over several periods

I have a couple weekly time series and an intervention occurred over several weeks and then for some, after a period of no intervention, began again. So, the pattern is off for a period of weeks, then ...
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72 views

Getting Residuals to be White Noise

I'm on a time series project for an undergraduate course. For the project I'm trying to come up with an ARIMA model for the housing starts data set. ...
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30 views

How do I estimate a time series regression using GMM in the way proposed by Acosta-Ormaechea and Morozumi (2013)?

In their paper Acosta-Ormaechea and Morozumi (2013) propose a use of GMM for estimating a regression in which they try to find the impact of reallocating public expenditure from some unproductive to ...
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59 views

Dynamic Time Warping for irregular time series

I have been reading a lot about Dynamic Time Warping (DTW) lately. I am very surprised that there is no literature at all on the application of DTW to irregular time series, or at least I could not ...
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61 views

Estimation of regression with autocorrelated errors

In a book it is written that, In regression work we typically assume that the observational errors are pairwise uncorrelated. But in most time series data , the successive residuals have tendency to ...
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55 views

Checking for seasonality in data set

I'm working on housing data set for a project for a undergraduate time series course. I'm trying to see if there is seasonality in the data. I used the following commands but do not know how to read ...
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44 views

is it possible a nonstationary time series, to produce a stationary ARMA model?

I Have a variable (time series) which is nonstationary. I found that from the graph which seems to have a stochastic trend and the correlogram has a typical nonstationary pattern. After that, I've ...
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36 views

How do I investigate how long it takes one variable to affect another in a time series

I am a total newbie when it comes to time series, so it is quite possible this question is duplicated somewhere else, only that I cannot find it because I don't know what this feature is called. My ...
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1answer
90 views

Filtering using a SARIMA model in R

I am not an expert in statistics, but I would like to work on a SARIMAX model representing power consumption. The exogeneous variable would be the temperature, but for now I found here I might need to ...
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41 views

Where can I find resources to learn about change-point analysis ?

Where can I find resources to learn about change-point analysis ? Hopefully, someone can advise me a textbook to read and it will cover both univariate change-point analysis and multivariate ...
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48 views

ACF and PACF plot analysis

I am new to ARIMA, and I am trying to understand these lag plots. Are the following ACF and PACF suggesting that the lag of my time series is 4? If I am wrong, please help me understand these plots. ...
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52 views

Arima model - multi step forecast

The following code shows a forecast of the next 24 hours of my electricity prices with two exogenous variables. My problem is, that I don't know how to build a forecast for the next 3 days or more ...
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36 views

Holt Winters Initialization Issue

I am using an additive seasonal Holt-Winters model to compute confidence band of my data. I followed the HW initialization process described by Rob J Hyn­d­man. The confidence band is derived by ...
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2answers
124 views

Capturing Seasonality in Multiple Regression for daily data

I have a daily sales data for a product which is highly seasonal. I want to capture the seasonality in the regression model. How I can do it? I have read that if you have quarterly or monthly data, in ...
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67 views

Two or more time series. What is the best way to test whether one of them is leading and by what time period?

I am trying to prove/disprove that one time series is leading trend for the other ones. Two time series are (probably) independent and the movements are caused by some (let's assume unknown) common ...
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References suggested for multivariate analysis of several similar time series

I have a time series dataset that reports the hourly page views and social media shares of online news stories. What I hope to obtain is the relationship between the two variables. I would imagine ...